A bowtie pattern

Geometry Level 4

Draw a triangle ABC, then denote the bisectors of BC and AC as M and N respectively. Now let P and Q be the bisectors of CN and CM respectively. Draw AM and BN (which are concurrent at F) and draw NQ and PM (which are concurrent at G). Shade in areas AFN, MFB, NGP and MGQ. If the shaded pattern continues to \({infinity}\) and the area of the triangle is \({360}\) then \({what}\) \({is}\) \({the}\) \({area}\) of the \({shaded}\) region?

(When I say that the pattern continues to infinity, I mean that the shaded bowtie's become smaller and their point of conconcurrency gets closer to C each time)

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